Math 3280 Differential Equations with Linear Algebra
Fall 2006
Prof. Peckham
Homeworks and Tests
Text: Differential Equations and Linear Algebra,
by Henry Edwards and David Penny, second edition, Pearson/Prentice Hall, 2005 (First Edition 2001). EC=Extra Credit problems; you may arrange with me to work on EC problems after the HW Set due date. Problems labelled as "additional" are not to be turned in, but you are expected to know how to do such problems.
- Set 1 Due Friday Sept. 8:
- Read Chapter 1: Sections 1.1, 1.2
- Section 1.1: 5, 6, 11, 16, 22, 32, 36, 41. EC: 45 (Hint: use 43.). Additional: 1, 8, 15, 17, 19, 27, 35, 37
- Section 1.2: 2,8,12,19,24. EC: 44 (suggestion: use Mathematica.). Additional: 1,31
- Lab 1 Introduction to Mathematica. Tuesday Sept. 5
Due Tuesday Sept. 12 to Joe Swintek.
Link to Lab 1 assignment.
Link to Lab 1 Mathematica Hints.
- Set 2 Due Friday Sept. 15:
- Read Sections 1.3, 1.4, 1.5.
- Section 1.3: 1-6 (photocopy of p26 provided in class), 13,14,17,18,21
- Section 1.4: 2,8,17,20,27
- Section 1.5: 2,4,10
- Lab 2: Introduction to Differential Eqations,
Tuesday, Sept. 12. Due Wed. Sept. 20 to Joe Swintek.
Link to Lab 2 assignment.
- Set 3 Due Friday Sept. 22:
- Read Sections 1.6 (pp 58-63 and 69-70), Chapter 1 summary, 2.1, 2.2
- Section 1.4: 36, 49, 51; EC: 69
- Section 1.5: 12,24,32,34,36; EC: 38
- Section 1.6: 2,22,23,46
- Section 2.1: 9.13
- Section 2.2: 1,4,14. For all 3 problems, ignore the book instructions.
Instead, construct a phase line diagram and use it to (i) describe the long term fate of solutions for ALL initial conditions, and (ii) sketch several representative solution curves.
- Set 4 Due Tuesday Sept. 26:
- Read Sec. 2.3 (skim pp 101-105), 2.4 (through Example 2)
- Section 2.3: 10
- Section 2.4: 1,10
- Lab 3: Comparing Graphical, Numerical, and Analytic Solutions to the Logistic Differential Equation.
Tuesday Sept. 20
Due Wednesday Sept. 27 to Joe Swintek.
Link to Lab 3 assignment.
Link to Lab 3 Separation of Variables Template.
Sample test 1 link
here.
Non graphical solutions
here.
- Exam 1: Chapters 1 and 2. Friday Sept. 29, 2006.
- Set 5 Due Friday, October 6, 2006
- Read Sections 3.1, 3.2, 3.3
- Section 3.1: 1, 14, 18, 19, 27, 33
- Section 3.2: 1, 4, 10, 11, 24
- Section 3.3: 4, 14, 15, 20, 21 (for 11 in Sec 3.2), 33, 34 (compare with p. 158)
- Lab 4: Applications of First Order Differential Equations: Falling object.
Tuesday Oct. 3,
Due Wednesday Oct. 11. to Joe Swintek.
Link to Lab 4-6 assignment.
- Set 6 Due Thursday, October 12, 2006 (No class Friday Oct. 13.)
- Read Sections 3.4 ,3.5, 3.6
- Section 3.4: 2, 5, 9. 13, 17, 24, 26, 31, 40
- Section 3.5: 1, 9, 12, 23, 34, 39 EC: 32
- Section 3.6: 1, 4, 11, 18, 21, 28, 33 (top row of A inverse only), 43, 52
- Lab 5: Applications of First Order Differential Equations:Compartmental
Analysis.
Tuesday Oct. 10,
Due Wednesday Oct. 18. to Joe Swintek.
Link to Lab 4-6 assignment.
Link to First Order Linear DE template.
- Set 7 Due Friday, October 20, 2006
- Read Sections 4.1, 4.2, 4.3
- Section 4.1: 1, 4, 7, 8, 9, 16, 21, 22, 25, 32, 33; EC: 41.
- Section 4.2: 4, 5, 9, 15, 20, 28.
- Section 4.3: 1, 2, 3, 6, 8, 12, 13, 19, 22; EC: 32.
- Lab 6: Applications of First Order Differential Equations: Parameter Matching..
Tuesday Oct. 17,
Due Postponed to Tuesday Oct. 31. to Joe Swintek.
Link to Lab 4-6 assignment.
Information on using ``sliders'' in Mathematica will be posted here later.
NOTE: Sliders on Mathematica has too many bugs to use. Rever to "trial and error."
- Set 8 Due Friday, October 27, 2006
- Read Sections 4.4, 4.7, 5.1, 5.2
- Section 4.4: 1, 2, 10, 12, 16, 17, 25
- Section 4.7: 1, 3, 5, 6, 9, 10, 13, 14, 15, 19, 23
- Section 5.1: 2, 3, 10, 14, 17, 33, 35, 40, 43, 44, 45; EC: 27, 52.
- Section 5.2: 1, 8, 13, 21; EC: 38.
Sample test 2 link
here.
Partial solutions are
here.
- Exam 2: Chapters 3 (secs 1-6), 4 (secs 1-4,7), 5 (secs 1,2)
and Lab 4-6 material.
Friday Nov. 3, 2006.
- Lab 7: Resonant Forcing of a Spring-Mass System
Tuesday Oct. 31 and Nov. 2.
Due date: Postponed to Thursday, Nov. 9 to Joe Swintek.
Link to Lab 7 assignment.
- Set 9 Due Friday, November 10, 2006.
- Read Sections 5.3, 5.4, 5.5, 5.6
- Section 5.2: 25, 26
- Section 5.3: 2, 9, 33, 39, 40, 42.
- Section 5.4: No problems assigned other than Lab 7.
- Section 5.5: 1, 2, 3, 16, 21, 22, 25, 30, 47 (turn in with set 10); EC: 57.
- Section 5.6: No problems assigned other than Lab 7.
- Set 10 Due Friday Nov. 17:
- Read Sections 6.1, 7.1 (skip Examples 5,6,7), 7.2, 7.3
- Section 5.5: 47
- Section 6.1: 1,13,23,27,36 (for 3x3 matrix only); EC 19
- Section 7.1: 1,2,8,24
- Section 7.2: 1,3,12,14,18,23
- Section 7.3: 1,9, 11 (For 1,9,11 - no computer tasks are required.), 17;
EC 27.
- Lab 8: Differential Equations and Linear Algebra with Mathematica
Tuesday Nov. 14, 21. Do in lab or submit writeup by
Wednesday, Nov. 22.
Link to Lab 8 assignment.
- Set 11 Due Friday Dec. 1:
- Read Sections 10.1 - 10.5
- Section 10.1: 1,7,16,19,23,27,29,38; EC 40.
- Section 10.2: 1,8.9.11
- Section 10.3: 1,5,11,12,18,27,30
- Section 10.4: 15, 18; EC: 29.
- Lab 9: Systems of Differential Equations: Phase plane analysis.
Tuesday, Nov. 28 and Tues. Dec. 5.
Due Wednesday, Dec. 6.
Link to Lab 9 assignment.
- Set 12 Due Monday Dec. 4:
- Section 10.5: 1,4,6,11,16,20; EC 25; EC: 32.
- Exam 3: Chapters 5,6,7,9,10, and labs on resonant forcing and phase planes. Details to be announced.
Friday Dec. 8, 2005.
A copy of the Laplace Transforms on the inside cover of the Penny and Edwards text will be provided.
Link to practice exam (without phase plane for last problem)
here.
Solutions are
here.
Review materials:
Abreviated course summary:
here.
Test 1 partial answers: here.
Test 2 partial answers: here.
Test 3 partial answers: here.
- Final Exam Tues. Dec. 19, 8:00-9:55 am in SCC 120!!!. Cumulative: Chapters 1 - 10 and labs.
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